Chiral metamaterials with negative refractive index based on four “U” splitring resonators

Zhaofeng Li,1 Rongkuo Zhao,2,3 Thomas Koschny,2,4 Maria Kafesaki,4 Kamil Boratay Alici,1

Evrim Colak,1 Humeyra Caglayan,1 Ekmel Ozbay,1,5 and C. M. Soukoulis2,4,a�

1Nanotechnology Research Center and Department of Physics, Bilkent University, Bilkent,06800 Ankara, Turkey2Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames,Iowa 50011, USA3Applied Optics Beijing Area Major Laboratory, Department of Physics, Beijing Normal University,Beijing 100875, China4Institute of Electronic Structure and Laser, FORTH, and Department of Materials Science and Technology,University of Crete, 71110 Heraklion, Crete, Greece5Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, 06800 Ankara, Turkey

�Received 5 February 2010; accepted 4 June 2010; published online 23 August 2010�

A uniaxial chiral metamaterial is constructed by double-layered four “U” split ring resonatorsmutually twisted by 90°. It shows a giant optical activity and circular dichroism. The retrieval resultsreveal that a negative refractive index is realized for circularly polarized waves due to the largechirality. The experimental results are in good agreement with the numerical results. © 2010American Institute of Physics. �doi:10.1063/1.3457448�

Chiral metamaterials �CMMs� have attracted much at-tention ever since it was predicted that negative refractioncan be achieved by a chiral route.1,2 In fact, CMMs also haveother interesting properties, such as the giant optical activityand circular dichroism, which may find their way into opticalapplications.3–8 As an artificial metamaterial, CMM lacksany mirror symmetry so that the cross-coupling between theelectric and magnetic fields exists at the resonance. The de-generacy of the two circularly polarized waves is therebybroken, i.e., right circularly polarized �RCP,+� waves andleft circularly polarized �LCP,�� waves have different refrac-tive indices. The chirality parameter � describes the strengthof the cross-coupling effect, so that the constitutive relationsof a chiral medium is given by

�D

B� = � �0� − i�/c

i�/c �0���E

H� , �1�

where �0 and �0 are the permittivity and permeability ofvacuum. � and � are the relative permittivity and permeabil-ity of the chiral medium. c is the speed of light in vacuum.Assuming a time dependence of e−i�t, the RCP�+� wave andLCP��� wave are defined as E�= �1 /2�E0�x� iy�.9 The re-fractive indices for RCP and LCP waves can be expressed asn�=n��,10 where n=���. When � is large enough, eithern+ or n− becomes negative. At the same time, both RCP andLCP waves have the same impedance of z /z0=�� /�, wherez0 is the impedance of the vacuum.

Since the beginning of the proposal of metamaterials,split ring resonators �SRRs� have played an important role inachieving negative permeability. Experiments showed thatSRRs can be used as magnetic metamaterials even at infraredand visible frequencies.11–13 Furthermore, a magnetic dimercan be formed by stacking two mutually twisted SRRs, andan array of these magnetic dimers can possess opticalactivity.14,15 However, due to the lack of the rotational sym-

metry, the optical activity is sensitive to the linear polariza-tion of the incident wave. To eliminate this shortage, wepropose here a design in which the U-shaped SRR pairs arearranged in C4 symmetry �see Fig. 1�. Thus, the constructedCMM is effectively uniaxial for the normal incidence wave.A related retrieval procedure6,16,17 can then be applied to cal-culate the effective parameters for our CMMs.

Figure 1 shows the schematics of the CMMs we study.The unit cell of the CMM structure consists of double-layered four “U” SRRs �Four-U-SRRs� patterned on oppositesides of an FR-4 board. This structure has been mentionedtheoretically18 and is discussed in another papers.19,20 Therelative dielectric constant of the FR-4 board is 4.0 with adielectric loss tangent of 0.025. The two layers of Four-U-SRRs are mutually twisted by 90°. The Four-U-SRRs arearranged so that the CMM structure possesses C4 symmetry.The dimensions of the unit cell and the photo of our experi-mental sample are shown in Fig. 1 and the caption.

In order to study the behavior of the chiral structure, weconducted numerical simulations and experiments. Thesimulation works were carried out by using CST MICROWAVE

STUDIO �Computer Simulation Technology GmbH, Darms-tadt, Germany�, wherein the finite integration technique was

a�Electronic mail: soukoulis@ameslab.gov.

FIG. 1. �Color online� �a� Schematic of a unit cell of the CMMs consistingof four “U” SRRs. �b� A photo of the experimental sample. The geometricparameters are given by ax=ay=15 mm, t=1.6 mm, d=1.5 mm, w=0.7 mm, and s=6 mm. The copper has a thickness of 0.03 mm.

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applied. The periodic boundary conditions were applied tothe x and y directions and the absorbing boundary conditionswere applied to the z direction. In the experiment, we fabri-cated the chiral structures with a dimension of 20 by 20 unitcells. The transmission coefficient was measured by an HP-8510C network analyzer with two standard horn antennas.

In order to study the transmission behaviors of the chiralstructure, in our simulation and experimental works, a lin-early polarized electromagnetic wave �E field in the x direc-tion� is incident on the chiral structure. On the other side ofthe structure, we measured the transmitted field in the x andy polarizations �Txx and Tyx�. Due to the fourfold rotationalsymmetry, circular polarization conversion is absent. Thetransmission of circularly polarized waves can be convertedfrom the linear transmission coefficients Txx and Tyx,

6,7 T�

=Txx� iTyx. For the transmitted EM wave, the polarizationazimuth rotation angle can be calculated as = �arg�T+�−arg�T−�� /2. The ellipticity of the transmitted wave is de-fined as =arctan��T+− T−� / �T++ T−��,9 which also mea-sures circular dichroism.

Figures 2�a� and 2�b� show the simulated and measuredtransmission spectra. There are obvious differences betweenthe transmissions of RCP and LCP waves around the reso-nances. Around the frequency of 5.1 GHz, the transmissionof LCP wave is 7−8 dB higher than that of the RCP wave.While around the frequency of 6.3 GHz, the transmission ofthe LCP wave is around 3−4 dB lower than that of the RCPwave. The fluctuations on the experiment curve come fromthe multiple reflections between the CMM structure and thehorn antennas.

Figures 2�c�–2�f� show the simulated and experimentalresults of the polarization azimuth rotation angle and theellipticity of the transmitted wave. It can be clearly seenthat, in the middle of the two resonant frequencies, the ellip-

ticity =0, where corresponds a pure optical activity effect,i.e., for the linear polarization incident wave, the transmis-sion wave is still the linear polarization but with a rotatedangle . The azimuth rotation angle is as large as 26° at 5.5GHz. The rotation angle per wavelength is 700° /�.

Figure 3 shows the retrieved effective parameters basedon the simulation and experimental data of the transmissionand reflection for one layer of the CMMs. In the retrievalprocess, the effective thickness of the CMM is assumed to be1.8 mm along the wave propagation direction. The chiralityis very large, e.g., it is 2.15 at =0. If using the followingexpression20

� = −��1��1�

�2 − ��12 + i �1��1�

+��2��2�

�2 − ��22 + i �2��2�

, �2�

to fit the result of the chirality �, it gives us ��1=0.22,��1=5.08 GHz, �1=0.02, ��2=0.28, ��2=6.42 GHz, and �2=0.03. Comparing Figs. 3�a� and 3�b� and Figs. 3�c� and3�d�, due to the relation of n�=n��, the strong chirality �can push the refractive index of RCP �LCP� wave to be nega-tive around the resonant frequency of 5.1 �6.4� GHz asshown in Figs. 3�c� and 3�d�. However, due to the losses inthe dielectric board, the figure of merit ��Re�n�/Im�n�� isonly around 1.1 �1.3� at 5.1 �6.4� GHz in the negative indexband. By using a lower loss substrate, the imaginary part ofthe negative index can be reduced. The figure of merit can belarger than 10 �not shown here�. In Figs. 3�e� and 3�f�, weshow the retrieved real parts for the permittivity and perme-ability of the CMM. Obviously, the Re��� is always positivethroughout the entire frequency range �except the tiny rangearound 6.4 GHz�, while Re��� is negative in the frequencyranges above the two resonances. In traditional metamateri-

FIG. 2. �Color online� Simulation and experimental results for the CMM.�a� and �b� are the transmission spectra for RCP and LCP waves. �c� and �d�are the polarization azimuth rotation angle . �e� and �f� are the ellipticityangle of the transmitted wave.

FIG. 3. �Color online� The retrieved effective parameters of the CMMsbased on the simulation �left� and experimental �right� data. �a� and �b� showthe real parts of the refractive index n and chirality �. �c� and �d� show thereal parts of the refractive indices for RCP and LCP waves. �e� and �f� showthe real parts of the permittivity � and permeability �.

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als, this will not result in a negative index. Therefore, thenegative index of RCP �LCP� wave is actually attributed tothe relatively small n and large chirality �.

In order to understand the mechanism of the resonancesfor our Four-U-SRRs CMM, we study the current modes onthe Four-U-SRRs. Figure 4 shows the simulated currentmodes at 5.1 and 6.3 GHz driven by the electric field in thex direction. At 5.1 GHz, the currents on the top and bottomFour-U-SRRs are in the same direction. On the contrary, at6.3 GHz, the currents on the top and bottom are in the op-posite direction. According to the current distribution, wecan analyze the induced magnetic field. Figure 4 shows thatthe x component of the induced magnetic field Hx is nonzero.And moreover, at 5.1 GHz, Hx and Ex are in the oppositedirections, while at 6.3 GHz, they are in the same direction.This causality between electric and magnetic fields is consis-tent with the constitute equation Eq. �1�.

In summary, by twisting the four “U” SRRs in the propa-gation direction, which owns the fourfold rotational symme-try, a uniaxial CMM can be constructed. We study the struc-ture via the numerical simulation and the experiment at 3.5−7.5 GHz. The simulation results agree with the experimen-tal results very well. This artificial structure gives us sostrong chirality that the refractive index of RCP or LCP canbe pushed to be negative at the vicinity of the resonance.

Such structure can be scaled to other frequencies. The pro-posed chiral structures are suitable for planar fabrication. Inthe future, we can use this planar design to contracture bulkCMMs via layer-by-layer method.

This work is supported by the European Union under theprojects EU-PHOME and EU-ECONAM, and TUBITAK un-der the Project Nos. 107A004 and 107A012. One of the au-thors �E.O.� also acknowledges partial support from theTurkish Academy of Sciences. Rongkuo Zhao acknowledgesthe China Scholarship Council �CSC� for financial support.

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FIG. 4. �Color online� The current distributions driven by the electric fieldin the x direction at 5.1 GHz and 6.3 GHz. The arrows in the middle of theSRRs show the direction of the x component of the induced magnetic field.

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